I've not tried fn_dblog on Express but if it is available the following will give you delete operations:

    SELECT 
    	* 
    FROM 
    	fn_dblog(NULL, NULL) 
    WHERE 
    	Operation = 'LOP_DELETE_ROWS'

Take the transaction ID for transactions you're interested in and identify the SID that initiated the transaction with:

    SELECT
    	[Transaction SID]
    FROM
    	fn_dblog(NULL, NULL)
    WHERE
    	[Transaction ID] = @TranID
    AND
    	[Operation] = 'LOP_BEGIN_XACT'

Then identify the user from the SID:

    SELECT
    	*
    FROM 
    	sysusers
    WHERE
    	[sid] = @SID

Edit: Bringing that all together to find deletes on a specified table:

    DECLARE @TableName sysname
    SET @TableName = 'dbo.Table_1'
    
    SELECT
    	u.[name] AS UserName
    	, l.[Begin Time] AS TransactionStartTime
    FROM
    	fn_dblog(NULL, NULL) l
    INNER JOIN
    	(
    	SELECT
    		[Transaction ID]
    	FROM 
    		fn_dblog(NULL, NULL) 
    	WHERE
    		AllocUnitName LIKE @TableName + '%'
    	AND
    		Operation = 'LOP_DELETE_ROWS'
    	) deletes
    ON	deletes.[Transaction ID] = l.[Transaction ID]
    INNER JOIN
    	sysusers u
    ON	u.[sid] = l.[Transaction SID]